Relative Stability using Simplified Routh Approximation Method (SRAM)

Abstract

A new Simplified Routh Approximation Method (SRAM) for model reduction of high order linear time-invariant systems is proposed. The Routh Approximation Methods for model reduction discussed in literature are based on α and β parameters. This paper presents a new method (SRAM) for model reduction involving only α-parameters to make the method simple. The proposed method is a direct method for deriving a kth-order approximant. The main advantage is that, in order to find the parameters of the kth-order approximant, it will no longer be necessary to previously obtain those of all pth-order approximants (p⩽k-1) as is the case with Routh Approximation Methods [3, 5, 6]. The additional advantageous feature of SRAM is that it always gives a stable reduced order model if the original system is stable. New algorithms are proposed to obtain the numerator and denominator polynomials of the reduced order models using only α-parameters, thus avoiding the use of β-parameters and recursive formulae. The method is illust...